help-0

[dawn wraith]

Have you heard of;
sin(x)=cos(pi/2-x)?

[hollow pelican]

nope im quite new to further trigo

[dawn wraith]

It’s the relation of sine and cosine in a right triangle

If you were to try and use a calculator, you’d get the same values!

[hollow pelican]

ok, ill try it out

[dawn wraith]

Make sure that if for example you want the sin of pi/6

The cosine is 2pi/6

The identity could also be written as:
sin(pi/2-x)=cos(x)

[hollow pelican]

i got diff values tho

[dawn wraith]

How though

Oh sorry

It’s 2 pi

2pi/6

[hollow pelican]

ohh ok

i got sin positive and cos negative value

[sage summit]

shockingly, it was discovered that pi is not the same as pi/2

[dawn wraith]

XD

Yeah, I noticed that thank you

[hollow pelican]

yea

[dawn wraith]

So without further ado, @hollow pelican
You may replace the cos(pi/2-theta) with just sin(theta)!

From there, you’ve got a pretty simple trigonometric equation

[hollow pelican]

ok

[dawn wraith]

Only now the question is, is there another solution?

[hollow pelican]

I am not sure

[dawn wraith]

Hint, another identity

Got any ideas?

[hollow pelican]

hmm is it

[dawn wraith]

Nope, pay attention.

[analog locust]

what's P()?

[dawn wraith]

don’t barge in like that bud, haven’t you noticed that we’re talking here?

[dawn wraith]

For you,
You might have never heard of the formula, sin(pi-x)=sin(x)

[hollow pelican]

oh yes

I didnt heard of that

[dawn wraith]

Use that to find the second solution, and you’re set!

[hollow pelican]

okay

[dawn wraith]

That should be all, is there anything else?

[hollow pelican]

no, thanks btw

[dawn wraith]

Anytime.

[pure hill]

is this channel free??

[sage summit]

it's true for any positive real number

[analog locust]

@dawn wraith oh sorry didn't noticed

[dawn wraith]

It’s fine.

[hollow pelican]

If i were to use this , is my working correct?

[sage summit]

yes

[hollow pelican]

ok thanks

[native temple]

if in conditional probability $$ P(B|A) = \frac{P(B) and P(A)}{P(B)} $$
and $$ P(B) = \frac{#Events}{Sample Space of A} $$
Since P(B) is being multiplied by P(A) and that is being divided out of P(A) doesn't that mean
$$ P(B|A) = P(B)?$$

[ocean seal]

Nerdy_Coder
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[glass lichen]

it's P(B and A)

not P(B) and P(A)

[native temple]

sorry let me fix that(but still answer my question)

if in conditional probability $$ P(B|A) = \frac{P(B and A)}{P(B)} $$
and $$ P(B) = \frac{#Events}{Sample Space of A} $$
Since P(B) is being multiplied by P(A) and that is being divided out of P(A) doesn't that mean
$$ P(B|A) = P(B)?$$

[glass lichen]

If A and B are independent, then yes, conditional probability is just P(B)

[ocean seal]

Nerdy_Coder
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[native temple]

oh

I see that's why it just doesn't say P(B)

because if they aren't mutaully exclusive....

[glass lichen]

Yeah..

[native temple]

then it's P(B)-P(A and B) right?

[alpine sable]

don't leave spaces between the $ and the code. use \text{} for the text and you can use \cap for the intersection sign.

[glass lichen]

There's channels to test the bots

[native temple]

Ahh makes sense

thanks

[warped phoenix]

seeing as to how you find the roots of a polynomial by setting it to 0, does that mean the roots are the x-intercepts?

[glass lichen]

yes..

[warped phoenix]

ok

[native temple]

obviously

[warped phoenix]

sorry my book is really shitty and didnt tell me that

[glass lichen]

roots, zeroes, x-intercepts are all equivalent

[warped phoenix]

they're teaching everything backwards and in the wrong order wtf
they show me a method in one lesson without explanation, then I have to spend an hour searching it up and learning it myself via youtube, only for them to explain it a couple lessons later

they "Taught" me synthetic division before long division of polynomials and i had to take like an hour to figure out wtf synthetic division was

and then they explain how to do it thoroughly like 4 lessons later

@glass lichen so root is just another word for x-intercept? or does it server another purpose

[glass lichen]

no

they're just equivalent terms

x-intercept is more general

[native temple]

$$text{Also use Ration Root(or Zero) Theorim as }\frac{p}{q} text{Helps you find the rational roots of ANY polynomial P = Leading Coefficent Q = Coefficent of Constant}$$

[ocean seal]

Nerdy_Coder

[glass lichen]

....

OR, you can just put the stuff that needs to be tex'd in dollar signs

[warped phoenix]

you dont need to put {text}, just put the $ before and after any math

yeah

[ocean seal]

Nerdy_Coder

$$\text{Also use Rational Root(or Zero) Theorim as }\frac{p}{q} \text{Helps you find the rational roots of ANY polynomial P = Leading Coefficent Q = Coefficent of Constant}$$

[glass lichen]

instead of fugly texs like that

also that's not what RRT says anyway

[native temple]

$$\text{Also use Rational Root(or Zero) Theorim as }\frac{p}{q} \text{Helps you find the rational roots of ANY polynomial P = Leading Coefficent Q = Coefficent of Constant}$$

[ocean seal]

Nerdy_Coder

[native temple]

sigh

$$\text{Also use Rational Root(or Zero) Theorim as }\frac{p}{q}
\text{Helps you find the rational roots of ANY polynomial P = Leading Coefficent Q = Coefficent of Constant}$$

[ocean seal]

Nerdy_Coder

[native temple]

there we go

[glass lichen]

can you stop spamming?

[native temple]

noooo

[warped phoenix]

Also use Rational Root (or Zero) Theorim as $\frac{p}{q}$ Helps you find the rational roots of ANY polynomial P = Leading Coefficent Q = Coefficent of Constant

[ocean seal]

TheMane3

[warped phoenix]

there @native temple

[gray isle]

is not what rrt states

[native temple]

oh thanks

[warped phoenix]

ik i just fixed the text for him

whats rrt btw?

[native temple]

rational root therim

[gray isle]

the acronym for rational root theorem

[warped phoenix]

oh ok

[glass lichen]

A polynomial P(x) has a rational root when $x=\pm\frac{p}{q}$, were q is a factor of the constant term and p is a factor of the leading coefficient

[ocean seal]

Mosh

[warped phoenix]

wait so all a root is is just the x-intercept

nothing more

[glass lichen]

yes

[warped phoenix]

"The roots of a polynomial are those values of the variable that cause the polynomial to evaluate to zero", wouldn't that just be what you put into f(x)? so in f(3), 3 is the root? the only value you can put in f(x) to make it equal to zero is f(0) though, right?

[native temple]

Oh I messed that up

[glass lichen]

if f(3)=0, then yes

[native temple]

https://www.mathwords.com/r/rational_root_theorem.htm

[warped phoenix]

ohhh

[meager pulsar]

Turn fractions into decimal numbers and sort results into exact decimals or periodic decimals with the calculations please

[warped phoenix]

f(3) would only ever equal zero if a, b, and c were 0 though :/

[glass lichen]

????

tf are you on about

[native temple]

I don't even understand the question

[glass lichen]

$f(x)=(x-3)(x-1)$, clearly $f(3)=0$

[ocean seal]

Mosh

[warped phoenix]

ohhh

sorry

[glass lichen]

likewise, clearly f(0)=3 in that case (coincidence it ended up being 3 and 0 swapping)

[native temple]

https://www.britannica.com/science/rational-root-theorem @warped phoenix

[warped phoenix]

How do I know if x is approaching negative infinity and positive infinity?

[native temple]

what?

oh

[warped phoenix]

It says to evaluate the function using a large negative and large positive number

but like...what's the threshold.

[native temple]

what function

I think you have to check transformations

[glass lichen]

just check end behaviours..

[warped phoenix]

what is that

this is the function

they evaluate using -1000, and 1000, should I always use those numebrs?

[glass lichen]

yeah, end behaviour is dominated by the leading term

so it's the same thing that happens to y=x^3

which is an odd power and positive co-efficient, so x->inf means y-> inf x-> -inf means y->-inf

[warped phoenix]

im not sure i follow...

wdym my leading term

[glass lichen]

the highest power term

[warped phoenix]

is (-1000)^3 and (1000)^3 the leading terms

oh ok

right

[glass lichen]

x^3 is the leading term..

[warped phoenix]

mhm

so since x^3 is positive, seeing as to how x isnt negative, x --> + inf.

[glass lichen]

x^3 is positive if x is positive..

[warped phoenix]

right

"Seeing as to how x isnt negative"

that means it approaches pos. infinity right?

but if x was negative, x --> -infinity ?

[glass lichen]

yes, for odd powers one end is +inf and the other is -inf

[warped phoenix]

because you have to evaluate the function with both a negative and positive number, got it

when they say "large pos/neg. number", what's the threshold for that?

anything above 1000?

[glass lichen]

literally any big number

[warped phoenix]

100's pretty big..

[glass lichen]

then use 100

[warped phoenix]

ohhhhhhhhhhhhhhhhhhh

😄

if x approaches negative or positive infinity, f(x) [so y basically] HAS to follow whatever one x is approaching right?

if x --> + inf., y --> + inf.

you said that before i think but i just wanted to make sure

[glass lichen]

no

end behaviour is reduced down to the same end behaviour as $y=\pm x^2$ and $y=\pm x$

[ocean seal]

Mosh

[glass lichen]

ie the leading term's degree's parity and leading co-efficient's sign

[warped phoenix]

whats parity

the sign in front of x?

[glass lichen]

even and oddness of an integer

[warped phoenix]

ahh

so how do i graph the function when x --> inf and x --> - inf

[glass lichen]

??

[warped phoenix]

like here

[glass lichen]

yeah, what about it?

[warped phoenix]

how do i know how far right and far left to go

[glass lichen]

the domain of a polynomial is R...

[warped phoenix]

whats a domain

also R is the remainder right

[glass lichen]

no..

R is the real numbers

[warped phoenix]

oh

[glass lichen]

domain is the input space

[warped phoenix]

wdym by input space

[glass lichen]

the space of values you can put into the function

you should've learned domain as one of the 1st things..

[warped phoenix]

LOL thats the first time im hearing this word (theres the shitty alg 2 book doing its work again)

so its what you substitute for x?

[finite spindle]

in other words, it's all possible values you can substitute for x. in this case, all real numbers from -infinity to infinity

[warped phoenix]

ohh

[glass lichen]

$D_f=\mathbb{R}$ for any polynomial f

[ocean seal]

Mosh

[finite spindle]

some functions for example, like f(x) = 1/x , won't let you put in x=0

so its domain would be all real numbers except 0.

[warped phoenix]

does that mean domain of a function = real numbers @glass lichen

[glass lichen]

no

[warped phoenix]

oh whats the f

[glass lichen]

"any polynomial f"

[warped phoenix]

ah so domain of a polynomial = real numbers

[glass lichen]

yes

[warped phoenix]

@finite spindle oh so the only two types of domains can be all real numbers, and all real numbers except 0?

[glass lichen]

No, clearly not

[finite spindle]

no, that was just one simple example

for example the function f(x) = 1/(3-x) cannot have x=3

[warped phoenix]

oh ok, wait, so if x MAKES the denominator equal 0 then you exclude it

oh ok

right

[finite spindle]

for example yeah

[warped phoenix]

ahh

[glass lichen]

$f(x)=\ln(x)\implies D_f=(0,\infty )$

[ocean seal]

Mosh

[warped phoenix]

what's ln

[glass lichen]

natural log

[warped phoenix]

(what's that 😅 )

[glass lichen]

anyway, back to the regular question...?

[dreamy mountain]

Log but with e

[warped phoenix]

idk what a log is

logarithm?

[wary stream]

Question: What about a polynomial that's a root? Like $f(x) = x^{1/2}$, that technically has a complex domain, unless I'm just over thinking it

[glass lichen]

it's not a polynomial

since $\frac{1}{2}\notin \mathbb{Z}^+\cup{0}$

[ocean seal]

Mosh

[warped phoenix]

ok, so, if the domain = any real number, basically what you're saying is I can choose how far left or right the graph goes?

after it hits the x int. ofc

[glass lichen]

yes, so long as the graph shows the intercepts / important features

[warped phoenix]

ohhhhhhhhhhhhhhhhhhh

awesome

why are all of you better teachers than a multi-million dollar company's online schooling program....LOL

[glass lichen]

yeah, sqrt(x) isnt a monomial, since it's not a non-neg integer power dldh

likewise with 1/x

[ocean seal]

dldh06

[glass lichen]

$p(x)=\sum_{i=0}^n a_ix^i$ is polynomials of degree n

[ocean seal]

Mosh

[wary stream]

Ah, whole numbers, makes sense

[glass lichen]

yeah

obviously you can write the binomial series for sqrt(x) and represent sqrt(x) as a poly

but sqrt(x) itself is not a monomial

[warped phoenix]

are you supposed to learn long division with polynomials before you learn synthetic division?

[glass lichen]

technically yes, synthetic is the shortcut

[warped phoenix]

welp my book did it the other way around 🥴

[serene hearth]

Can someone explain how they found the value of X and T

I'm particularly interested to know how they ended up on the hyperbolic functions

[vague coral]

The characteristic equation is, for the first one,
r^2 + n^2 = 0
r^2 = -n^2 = (in)^2
r = in or r= -in, with i^2 = -1
With those conditions, they applied a formula which is the solution of the differential equation when solutions of characteristic equation are complex numbers

[serene hearth]

I see

but isn't that normal sin and cos

Im assuming u mean this formula

[vague coral]

yes but you can do some works to get cosh and sinh

since cosh =( e^x + e^-x)/2

wait no

[serene hearth]

no I do not xD

[vague coral]

Its cosh(ix) = cosx

They used that to get the solutions with cosh and sinh

[serene hearth]

ohh I see

But isn't that an additional burden

why not let it stay as cos and sin

[vague coral]

It depends of the exercise, it can simplify calculation

[serene hearth]

hmm

[vague coral]

You only have cosh and sinh, instead of exp and cos and sin

its much better for calculation

I saw physics exercise where we needed to use cosh and sinh

[serene hearth]

I see, that clears it!

Thanks :)

[vague coral]

np

[digital rapids]

i just started using matlab, and i came accross this

[J, grad] = lrCostFunction(theta_t, X_t, y_t, lambda_t);

im not sure what this notation means

[wary stream]

Which part?

[digital rapids]

theta_t = [-2; -1; 1; 2];
X_t = [ones(5,1) reshape(1:15,5,3)/10];
y_t = ([1;0;1;0;1] >= 0.5);
lambda_t = 3;
[J, grad] = lrCostFunction(theta_t, X_t, y_t, lambda_t)

Oh

is it that the function on the rhs produces two outputs

and J is the first and grad is the second?

[wary stream]

Yes, exactly

[digital rapids]

mb i thought [J, grad] was a matrix but i wasnt thinking straight

[wary stream]

Stores outputs of function into variable named "J" and "grad" respectively

[heady tusk]

pretend that is a parallelogram, would those to corners be the same

those two angles

yes? no?

[digital rapids]

yeah cos the sides are parallel right

[heady tusk]

yes

of of course yes

I'm stupid lol

[alpine sable]

Can someone please explain how

What formulas are u used here?

[glass lichen]

algebra then triple angle

[alpine sable]

Umm what?

[glass lichen]

Gonna need a better question than "what?"

they did algebra... then did triple angle

[alpine sable]

I understand they used triple angle formula with sin

But i don't understand how they used it with cos

[warped thunder]

Can anyone teach me how to divide nos with cancelling them out

[alpine sable]

Cos3x = 4cos³x -3 cosx
But here we have 4cos²x-3cosx

How do they do it?

@glass lichen

[glass lichen]

typo

[alpine sable]

Where

[glass lichen]

the line prior....

the 2 should be a 3

simple.

[alpine sable]

Ah

How they do it in the first line??

[glass lichen]

what?

"it" is so specific

[alpine sable]

How did they get
Cos(3-4 cos² t)

[glass lichen]

simplifiying with algebra

[alpine sable]

I don't understand i am sorry

[glass lichen]

have you done algebra before?

[alpine sable]

What formula did they use?

[glass lichen]

NONE

they did algebra

not everything is a formula

[alpine sable]

Can u give me an example of what they used?

[glass lichen]

.....

$3x+1-2x+7=x+8$

[ocean seal]

Mosh

[alpine sable]

Oh

I understand now

Than you so much

Is it free?

[balmy thistle]

wah i was typing :C

[alpine sable]

@balmy thistle yeah, I saw that, go ahead.

[balmy thistle]

hi ive got a few questions for an upcoming oral exam.

1. whats the argument of sine and cosine?
2. are there implicite functions you cant transform into explicite functions without information being lost? name examples.
3. why is it useful to translate implicite into explicite forms?

thank you in advance 🙂

[rigid smelt]

hmm is it supposed to be the answer for that exam?

[balmy thistle]

no for self test

[glass lichen]

are these the questions on the exam or designated practice questions?

[balmy thistle]

practice questions, i dont have the exam questions they are in 3 weeks from today

and i wont ask them here lol

[glass lichen]

Ok, so post your explanations/answers and someone can read it and comment on it

[wary stream]

What's the exact question?

More context is needed than a chart of values

[balmy thistle]

i srsly dont know the answers to it thats why i asked here to memorize them 😦

[wary stream]

Memorizing answers is not the best way to study

[balmy thistle]

but these questions are knowledge questions only o:

[wary stream]

It's based on your own knowledge, not others

[balmy thistle]

i googled already and found no answer thats why i came here in search of help 😦

[wary stream]

It also helps if you spelled "sine" and "cosine" properly too

[balmy thistle]

im from russia sorry for my english

[chrome monolith]

Is the derivative

4x - cos 5x^2/2 ?

Some1 please answer quick

[wary stream]

Why quick?

[chrome monolith]

I have an exam in a hour

[chrome monolith]

?

[wary stream]

The trig part looks wrong

[chrome monolith]

Whg

Why

[wary stream]

Because it's sin(5x)

[chrome monolith]

Isnt the integral of sin ( - cos x)

[frosty drift]

hey what's up, can you help me solve this?
9x - 7i > 3 (3x - 7u)

[wary stream]

Channel busy

[chrome monolith]

4x - cos 5x

[wary stream]

Also use u sub

[chrome monolith]

?

[wary stream]

For this

[chrome monolith]

Do u know the ans

[wary stream]

No

I mean u sub for sin(5x)

[chrome monolith]

The ans key has 4x - cos 5x/5

Idk how

[chrome monolith]

We havent learned u sub

[wary stream]

Like I said u sub

U sub is kinda like inverse chain rule

[chrome monolith]

Uh

Mann idk what to do

[wary stream]

Google it

[chrome monolith]

,w integral (4 + sin 5x)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by heyguysimhere#7917

[wary stream]

That's what you said the answer key said

[chrome monolith]

Yh

Idk how they got it tho

Lolol

[wary stream]

Use u sub for the trig part

[chrome monolith]

Idk how to

[wary stream]

Google it. You can learn the concept in like 10 minutes rather than have someone explain it for an hour

[glass lichen]

$u=5x\implies \dd{u}=5\dd{x}$

[ocean seal]

Mosh

[chrome monolith]

?

[wary stream]

Mosh just showed you u sub

[chrome monolith]

Yeah

Doesnt help

[glass lichen]

have you done integrals of trig before...?

[chrome monolith]

Yh

[glass lichen]

so you can integrate sin(x)?

[wary stream]

Literally, if you don't understand the concept, and this pointless back and forth of you not understanding and people trying to explain, because you apparently have less than an hour, as you stated, Google u sub and watch videos on it

[chrome monolith]

Yeah

[chrome monolith]

• cos x

[glass lichen]

+c but yeah

[chrome monolith]

Yeah

[glass lichen]

and yeah, google u-sub if you werent taught it..

or just ask what differentiates to sin(5x)

[chrome monolith]

I dnt have time to learn a new concept now

[glass lichen]

well I doubt it's new given you're being asked about it...

so it must've been taught.

[chrome monolith]

My teacher never taught it

😂

[glass lichen]

I doubt that, but anyway

[chrome monolith]

Bruh

[glass lichen]

just google u-sub or reverse chain rule

[chrome monolith]

Yeah so what do i do with that

[glass lichen]

with what?
I was just seeing if you at least knew how to integrate trig.

[chrome monolith]

Bro

[glass lichen]

You've already been told it's u-sub

[chrome monolith]

I need help solving the problem

[glass lichen]

and I helped you

[chrome monolith]

With what

[glass lichen]

I did the u-sub part for you...

[chrome monolith]

Asking me how to integrate sin

[glass lichen]

$u=5x\implies \dd{u}=5\dd{x}$

[ocean seal]

Mosh

[glass lichen]

That's u-sub

[chrome monolith]

How do i apply it to the question

[glass lichen]

do the sub...

[wary stream]

This is exactly what I mean by the pointless back and forth conversation of a concept you don't understand

[chrome monolith]

I just want to know why its over 5

[glass lichen]

$\int \sin(5x)\dd{x}=\int\frac{1}{5}\sin(u)\dd{u}$

[ocean seal]

Mosh

[chrome monolith]

So

• cos 5x / 5

[glass lichen]

+c, yes

[primal dew]

what is the 0 root of 1/0

assuming 1/0 is defined

[dawn wraith]

You’re basically asking what’s
1/0^(1/0)

[abstract breach]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[primal dew]

this is what i was solving

[dawn wraith]

Hmm

Defined as what though

[primal dew]

a new number that I call z

[dawn wraith]

So z to the zth power

[primal dew]

yes

[dawn wraith]

That should be it?

[primal dew]

but what is z^z

[glass lichen]

no fucking clue

you're the one defining z

[primal dew]

well z is 1/0

z is a zeroth

[glass lichen]

Im aware z:=1/0

[dawn wraith]

What does it mean when you raise something to the zth?

[glass lichen]

but by your construction it's just z^z

[primal dew]

wdym?

[dawn wraith]

You defined zed to be the number 1/0

[primal dew]

yes

[dawn wraith]

I do not know how to calculate a number in which is raised to that power

Only you can, for the reason that you defined the number itself

[primal dew]

ok what happens when you have a 0th root

[glass lichen]

no clue, 0th root doesnt exist in standard math

[dawn wraith]

Impossible, it’s like raising it to the power of something that is divided by 0

[glass lichen]

since 1/0 is an undefined object, you are giving it a definiton and thus need to define 0th root

[dawn wraith]

Smart words that he said^

[glass lichen]

However also in your construction you have that 1=0

[spark shadow]

Is someone free here

[primal dew]

this is all i have

[spark shadow]

I need help

[dawn wraith]

That’s also true, it’s a contradiction.

[dawn wraith]

Channel occupied, sorry.

[glass lichen]

$\frac{z}{z}=1, \forall z\neq 0$

[ocean seal]

Mosh

[primal dew]

where?

[glass lichen]

z/z = 0 on your ss, however z/z = 1 since z isnt 0

[dawn wraith]

Anything that you divide by itself will result in the number 1

[glass lichen]

anything non-zero

[primal dew]

but z/z = 1/0 * 1/0

and i did the math

[dawn wraith]

Yeah, obviously

[primal dew]

and got 0

[dawn wraith]

Which means you’ve got a contradiction

[primal dew]

but can z be treated as non-zero?

[glass lichen]

holy

[dawn wraith]

You define that

It’s your number

[glass lichen]

z is your number

I dont give a fuck about z

Your system that includes z looks to be equipped with operations from the real numbers, thus z/z=1

[primal dew]

but

[glass lichen]

yeah, so you showed 1=0 in your system

since you are using facts about rational/real numbers

either z acts as 0 or as z

[dawn wraith]

Hold up bud you’ve gone a step forward

[primal dew]

what?

[dawn wraith]

You’re saying 0/0 * 1/0 is 0/0 * z

But 0/0 is undefined

[primal dew]

0/0 is 0 zeroths

so 0/0 = 0

[glass lichen]

wheel algebra moment

[dawn wraith]

Okay, but you have a contradiction

So you’ll have to do something about it

[primal dew]

what could i do?

[glass lichen]

It's your system

[dawn wraith]

Redefine 0/0

You do what you want

[glass lichen]

This is like JK Rowling asking a random person to write the next Harry Potter

[primal dew]

i mean i could say 0/0 = 1 but thats sounds very wrong

[glass lichen]

oh and z=1/0 means perfect sense...

[dawn wraith]

Well, your system, your rules.

Go ahead and define it, it’ll hopefully fix the contradiction

[primal dew]

if 0/0 = 1 then z/1 = 1 and sqr z/z = 1

but ill do that

[dawn wraith]

Good!

[primal dew]

wait

no

z -z would = 1

[glass lichen]

Yeah, this is why 1/0 stays undefined

[dawn wraith]

XD

[glass lichen]

cause assuming it is defined causes things to break

[primal dew]

or i could just say that z is not non-zero

[glass lichen]

so z=0

[dawn wraith]

And then you get 1=0

Since z = 1/0

[primal dew]

no if z is not-non zero it just means non-zero is a set of numbers

[dawn wraith]

Ugh

[glass lichen]

Im gonna say this bluntly: you are trying to define a system, it makes no sense to be asking other people on how the system works.

[primal dew]

well im trying to see if the system works

[glass lichen]

it doesnt

cause you have simply taken the real numbers and added a new element in without redefining the operations.

• and * you're using act on R, not R w/ {z}

[primal dew]

wait the 0th root of 1 is 1

[dawn wraith]

?

so 1^z is 1, okay

[primal dew]

i guess

[spring sierra]

how would you approach this question

[alpine sable]

a) sine rule

[spring sierra]

because I've tried the sin rule

angle A is 51.1

but if that's 51.1

it means the angle on th eother side is obtuse

and since it's isosceles

that would make two angles obtuse?

in a triangle

[alpine sable]

wdym the other angle

what angle

[spring sierra]

those two

[dawn wraith]

pay attention

there are 2 possibilities

[spring sierra]

oh

do i take away

from 180

[dawn wraith]

due to the identity
sin(180 - x) = sin(x) existing

[spring sierra]

OH YEAH

thank you

[dawn wraith]

piece of cake

[short sand]

Okay, practical question.
I have a set of products that sell at a known velocity.
I represent this velocity as a decimal of capacity in slots.
For example, Product A sells 0.1 slots per day. After 10 days it will sell through 1 slot.
A store has a set positive integer number of slots. 23, for example.
I can set the quantity of products in a store as a positive integer number of slots.
I want to set the slot quantity for each product in such a way as the minimum days of any individual product is as high as possible.
Sample set: A: 0.1 slots/day, B: 0.25 slots/day, C: 0.1 slots/day. D: 0.55 slots/day, E: 0.75 slots/day
Slot Capacity: 27

[civic elbow]

Confused on how to do these 2 problems

[minor heath]

similar triangles

[civic elbow]

Wait would the second one be h?

[warped flower]

ASA or SSS rules

[minor heath]

just a hint that all those right triangles, the two triangles and the entire triangle itself, are similar to each other

[civic elbow]

Still a little confused

If you can, could you maybe explain how to do one of these problems?

[minor heath]

ok first can you orientate each triangle in the figure such that they look similar?

[civic elbow]

Ya EHG

EHF*

And GED

[minor heath]

and then the last one?

[civic elbow]

FDJ

[minor heath]

wrong side order, since you did each in (shorter side, longer side, hypotenuse)

just apply that to the triangle you named

[civic elbow]

Ah

So I am a little confused what to do next

[minor heath]

ok now, pick two triangles that include side j, and include side g, to answer the first question

[civic elbow]

We can use FJD and GED

[minor heath]

DFJ* (remember that side order)

[civic elbow]

Ah ya

[minor heath]

now, use this property of similar triangles: (chosen side of 1st triangle/same side of 2nd triangle) = (another chosen side of 1st triangle/same other side of 2nd triangle)

for example, you can set d/j = e/f

[civic elbow]

j/d=d/g?

[minor heath]

ok now you get it

then apply that to the next question

[civic elbow]

Second one then is h?

[minor heath]

ok

yea i think thats it

[civic elbow]

Is it ok if I show 2 more

[minor heath]

sure

[civic elbow]

I think I know the answers

Just want someone to check

[minor heath]

kk

[civic elbow]

Think j and h?

[glass lichen]

yes

[minor heath]

yea

[lone dagger]

Could someone explain me this step?
I know it should give -0,4, but that's not the issue. How do you even get the 0,4?

[thorn kindle]

,calc 1/2.5

[ocean seal]

Result:

0.4

[lone dagger]

Oh

xD

[thorn kindle]

But it should be -0.4

[lone dagger]

Gotta get my brain ready for the test tomorrow.

Thanks haha

[thorn kindle]

,calc (1/10)^(-1/2.5)

[ocean seal]

Result:

2.5118864315096

[thorn kindle]

@lone dagger not 0.4

-0.4

[lone dagger]

Yep I know that is wrong xd

[thorn kindle]

Alr

Gl

[lone dagger]

Thank you

[tiny agate]

hey guys, i have a differential geometry question but i figured it could be a little advanced so i asked in topology-and-geometry, it's an exercise my professor solved that i didn't get, can anybody take a look?
thank you!

[loud iris]

find general solutions of sinx + cosx = 2^1/2

can someone help me out ?

[rigid smelt]

If you divide sqrt(2) on both sides

You will notcie a very particular patterns

sin(pi/4)=cos(pi/4)=1/sqrt(2)

[loud iris]

hold up wait

maybe 2 mins

[rigid smelt]

Now substitute this into
sin(x)/sqrt(2)+cos(x)/sqrt(2)=1

[loud iris]

lemme absorb what u said

[rigid smelt]

Sure

We are making use of the addition identity here

[loud iris]

pls elaborate this i have no clue as how we came here

[rigid smelt]

Ok dont focus on that too much

[rigid smelt]

are you clear on this?

[loud iris]

yup

[rigid smelt]

Alright

So you also know that sin(pi/4)=1/sqrt(2) right?

[loud iris]

yea

that makes it sinxsinpi/4 + cosxcosi/4

ok

[rigid smelt]

So we can rewrite the equation as sin(x)sin(pi/4) + cos(x)tsqrt(2)=1

[loud iris]

i think i got it

[rigid smelt]

Yeah

[loud iris]

we can then move on to convert this to cos(x-pi/4)

yeap

thanks

[rigid smelt]

Basically this is a method of solving equations in the form asin(x)+bcos(x)=c

[loud iris]

im good to go

[loud iris]

yea ik im doing qs related to that only

mind go poof at times disables me to think about simple algebra at times

[rigid smelt]

Well if you are interested, the first to doing that is dividing both sides by sqrt(a^2+b^2)

And the steps later on are just what we did

[loud iris]

isnt that used to find r

like

[rigid smelt]

Yes kind of

[loud iris]

a=rcosy and b=rsiny

like that

where

[rigid smelt]

The idea is that we want to convert it into sin(x +/- y) or cos(x +/- y)

[loud iris]

r=(a^2 + b^2)^1/2

[loud iris]

yes man got it

thenks

[loud iris]

...

@rigid smelt bruh

im getting wrong ans 😭

[loud iris]

i tried this approach as well

[warped phoenix]

for y = kf(x), the function is stretched away from the x axis if k > 0, compressed towards the x-axis if 0 < k < 1, and reflected across the x-axis if k > 0, right?

just to make sure im saying that right

[warped phoenix]

<@&286206848099549185>

?

anyone?

[queen wigeon]

if 0<k<1, the function is compressed, if k > 1, the function is stretched away from the x-axis, and it is reflected over the x axis if k < 0

[warped phoenix]

ah ok

[ocean seal]

TheMane3

[warped phoenix]

why do you shift the graph to the right two units when inside the parenthesis the 2 is negative? @queen wigeon

shouldn't it be moved two units to the left since f(x + k) is shifted to the right whereas f(x - k) is shifted to the left?

[inner adder]

hello

i have some question it is not in math but i hope someone can help me :/

its on german hope someone you unserstand with translator or somethink

[warped phoenix]

ok disregard my last question then

how do they know that g(x) = f(x + 2) + 7 ?

it doesn't say that anywhere in the question

[inner adder]

its on german

Subject: Technology

[glass lichen]

cause f(x) is x^2

so (x+2)^2 is clearly f(x+2)

[warped phoenix]

$(x +2)^2 = (1x+2) (1x+2)$

[ocean seal]

TheMane3

[warped phoenix]

$(1x+2) (1x+2) = x^2 + 4x + 4$

[ocean seal]

TheMane3

[warped phoenix]

so wouldn't it be $f(x + 4x + 4)$?

[ocean seal]

TheMane3

[glass lichen]

No....

f(x)=x^2

[warped phoenix]

but in (x + 2)^2 the degree isnt being directly distributed to x

[glass lichen]

ik

so?

[warped phoenix]

so how can it be x^2

[glass lichen]

x+2 is being squared

correct?

[warped phoenix]

right

[glass lichen]

so if f(x)=x^2, f(x+2)=(x+2)^2

cause all f does is square whatever you put into it

[warped phoenix]

ahh

[nimble meteor]

I'm so confused why do we have to use double angle identities?

like can't we just find the cos of an angle and then just multiply it times two?

[oak chasm]

Because if you get a cosine of 1, double that is 2, right?

[nimble meteor]

yeah

[oak chasm]

But you can't get a cosine of double the angle that's 2, right?

Because cosine only goes up to 1.

[nimble meteor]

oh yeah

oHHHHHHHHHHHHHHH

dang that actually makes sense

THANKSSSSSSSSSSSSSSSSSSSSSSSSS

[oak chasm]

No problem.

[nimble meteor]

dang your smart lol

[alpine sable]

I want to say that I computated something incorrectly but cannot see any mistakes

Not sure where the difference between -17 and -34 (my answer) comes from

ait

wait

I think my error is I set it = 0 not = 17 or something along these lines

Would love if someone can confirm this for me

[lilac raptor]

If you have two numbers and you add those two numbers than the numbers that you added have numbered the second number that has just been added due to the subtraction of the first number that was numbered by the first number.

true?

[glass lichen]

what

[wind swallow]

what

[sour pasture]

@alpine sable that’s right, your error is what you set it equal to.
the RHS should be (w - w_0)

@lilac raptor
are you are saying if a + b = c,
Then b = c - a?

[alpine sable]

Thanks!

whats the best textbook for practice questions for calc I and II?

[vestal hollow]

Try #book-recommendations

[alpine sable]

didnt even see that channel, thanks!

[vestal hollow]

How do you do this? I've looked at some examples and I don't get it

How do you even do the base case? Do you sub in n, k = 1? Bc I saw some using n = 1 and k = 0, 1

[muted raft]

you are inducting on n

not on k

or rather proving k follows from inducting n

[vestal hollow]

Is this oaky so far?

How am I supposed to show that it's an integer?? The sum of two integers is an integer but that requires showing that n choose k and n choose (k-1) are also integers, which is what I'm trying to do

[gusty ravine]

your statement is P(n): n choose k is an integer for k where 0<= k <= n

[glass lichen]

You use a strong hypothesis keep in mind

[gusty ravine]

prove P(1) to be true. Assume P(i) is true and deduce P(i+1) gg

[glass lichen]

you did the n=1 case, then assume it holds for n=j, then show n=j+1 is true

[alpine sable]

hey

[glass lichen]

$\binom{j+1}{k}=\binom{j}{k-1}+\binom{j}{k}$

[alpine sable]

i got a calc question

[ocean seal]

Mosh

[glass lichen]

in use.

clearly

[alpine sable]

can i ask here

ok

[glass lichen]

the 2 co-efficients on the RHS are integers by the hypothesis, and sum of integers is an integer

[vestal hollow]

Wait I'm an idiot LOL by "by the hypothesis" you mean the part where I say "assume it holds for n = j" right?

[glass lichen]

You need a strong hypothesis, so $\binom{j}{k}\in\mathbb{Z}, 0\leq k\leq j$

[ocean seal]

Mosh

[vestal hollow]

That's what I did here right?

[glass lichen]

yes

[vestal hollow]

Just making sure bc it looks the same

Sweet

Then I think I'm done

[glass lichen]

yeah it's just 2 lines

[vestal hollow]

Maybe I shuld include a closing statement

But everything else is okay?

[glass lichen]

yeah

[vestal hollow]

Sweet, thanks Mosh

[obsidian marsh]

sl e

someone who knows Mathematica can tell where my plot is?

lol

[oak chasm]

@obsidian marsh What's the domain of e^t?

,w Table[N[5(1 - e^(-5000t))], {t, 0, 25000, 2500}]

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Chai T. Rex#7323

[oak chasm]

Looks like you should be looking around y = 5 or so.

,w Plot[5(1 - E^(-5000x)), {x, 0, 25000}]

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Chai T. Rex#7323

[oak chasm]

@obsidian marsh ^

[rocky axle]

had this come up in a test the other day and everyone failed to get it right
I'm wondering how to go about solving this

[sleek elbow]

bro what is that im definitely not qualified in the slightest to do that

[clever locust]

Well notice that

$$\int_{-\infty}^\infty \frac{\dd{x}}{1+4\pi^2(x-5000)^2} = \int_{-\infty}^\infty \frac{\dd{x}}{1+[2\pi(x-5000)]^2}$$

Then do the substitution $u=2\pi(x-5000)$, $\dd{u}=2\pi \dd{x}$, so you have

$$\frac{1}{2\pi} \int_{-\infty}^\infty \frac{\dd{u}}{1+u^2}$$

From there you should probably be able to do it yourself

[ocean seal]

Lorago

[timid wind]

ok?

[clever locust]

Does that make sense?

[rocky axle]

yup thank you

[clever locust]

Np

[strong crater]

why does the answer take the reciprocal of tan?

the description even says that since (3pi/2 + theta) is in the 4th quadrant so shouldn't it be -tan?

[oak chasm]

@strong crater Because tangent is the slope of an angle. When you add 3/2 pi to an angle, it's perpendicular to the original angle. What happens to the slope when you find the perpendicular slope?

If the original slope is m, what's the perpendicular slope?

[strong crater]

-1/m

[oak chasm]

Right, so if the original slope is tan(theta), the perpendicular slope is -1/tan(theta).

[strong crater]

ohhhh i see

okie thanks

[oak chasm]

No problem.

[bold shard]

i have a question about using the standard normal probabilities table. I have to look up the probability that : P(-1.72 < Z < 1.22) , and im not sure how to go about doing this. I thought that you subtract (1.22 - [-1.72]) and then look up the answer in the table but that was wrong.. any help?

[bold shard]

<@&286206848099549185>

[slate monolith]

ask it in stats

they can prob be of more help

[bold shard]

ight

[rocky dock]

the 1st screenshot is my solution to the question above

any ideas why im wrong?

[slate monolith]

16 should be fine

cause its 4 + 4

no negative numbers

so

[0, infinity)

sqrtx can never be -4

unless imaginary

[rocky dock]

hmm i dont quite understand

why was my interval notation incorrect?

[slate monolith]

so u said sqrtx + 4 =/ 0

that will always be true

since the sqrt of a pos number

is always positive

the only issue comes when x < 0

which you mentioned

[rocky dock]

oh, so if it's a problem like this

the domain will always be [0,∞)?

[slate monolith]

the denominator will never be 0

and it will only not exist when x < 0

so yes

[rocky dock]

ok, so the +4 ensures it'll never be 0

[slate monolith]

yes

[rocky dock]

so if the x was a normal x and not the sqrt

it would have to be > 0 only right?

[slate monolith]

yes

well

both of them?

so x - 2 / x + 4?

or just 1

[rocky dock]

both and just 1 if you dont mind explaining the diff

[slate monolith]

okay so

if both

then its for all x but x = -4

cause thenu have -6/0

vertical asymptote

if sqrt on top but not bottom

[0, infinity)

if just on top

same thing as well

[rocky dock]

ok

appreciate the help!

you rock!

[slate monolith]

sure thing 🤘

[boreal sinew]

Does theorem corresponding to the last line have a name?
$$
\begin{equation}
\begin{cases}
f: X \to Y; \
g: Y \to Z; \
f^{\rightarrow}(S_x) = { y \in Y : \exists x \in S_x. y=f(x) } \
g^{\leftarrow} = { z \in Z: \exists y \in Y. z=g(y) } \
[g \circ f]^{\rightarrow}(S_x) = { z \in Z: \exists y \in f^{\rightarrow}(S_x) \cap g^{\leftarrow}. z=g(y) } \
[g \circ f]^{\rightarrow}(S_x) = [g_{\vert f^{\rightarrow}(S_x) \cap g^{\leftarrow}} \circ f^{\vert f^{\rightarrow}(S_x) \cap g^{\leftarrow}}]
\end{cases}
\end{equation}
$$
Note: $g_{\vert S_y}$ is domain restriction of $g$ to $S_y$ while $f^{\vert S_x}$ is corestriction of $f$ to $S_y$. I.e.
$$
\begin{equation}
\begin{cases}
f^{\vert S_y}: X \to S_y \
g_{\vert S_y}: S_y \to Z
\end{cases}
\end{equation}
$$

[ocean seal]

JohnDark
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[boreal sinew]

Note: $g_{\vert S_y}$ is domain restriction of $g$ to $S_y$ while $f^{\vert S_y}$ is corestriction of $f$ to $S_y$. I.e.
$$
\begin{equation}
\begin{cases}
f^{\vert S_y}: X \to S_y \
g_{\vert S_y}: S_y \to Z
\end{cases}
\end{equation}
$$

[ocean seal]

JohnDark
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[wicked axle]

can I get some help on this?

[slate monolith]

oooh i did this exat problem

[wicked axle]

:o

help help! :D

[slate monolith]

lemme see

[wicked axle]

so what ive done so far is find the coordinates of B

we also know the x and y intercepts of the line

im confused where to go from here

or if im even on the right track

[slate monolith]

u gotta find the slope between A and B

the x intercept is C

u gotta find C as a function of r

show me what u got

[wicked axle]

one sec let me try and do it on paper this time

[boreal sinew]

Please, don't break rules next time.

2. Before asking a question, make sure that the channel you are using is not currently in use. An occupied channel would generally have an ongoing discussion or a trailing unanswered question. Likewise, when you are done using a channel, make this clear so that it's open for others to use.

[slate monolith]

nobody had typed in 20 min

so like 🤷‍♂️

[boreal sinew]

Indeed, my bad

[jagged imp]

there are other open channels, and 20 minutes isn't that long

plus they'd already posted in precalc

[slate monolith]

true

hmm

[wicked axle]

i mean no one typed that they were done using this channel

and like the other guy said no one had typed for a while

[slate monolith]

lets just move on

pahul did u get any work on paper

[wicked axle]

yeah gimmie sec still doing some work

[boreal sinew]

@slate monolith Where would you suggest me post the question that I posted here earlier? It is about function composition, domain restrictions and corestrictions. The topic of function composition is at basic level is covered in Intermediate algebra course here (https://www.mesacc.edu/~scotz47781/mat120/), but I'm unsure to which branch of mathematics it actually belongs because functions and their compositions are ubiquitous.

[slate monolith]

if I understand what youre saying, this isnt linear algebra, and prealgebra might not be so helpful so this is a good spot
maybe in questions-1

[boreal sinew]

I'll copy the question from here to there, thank you! @slate monolith

[slate monolith]

np

[wicked axle]

so should I be trying to find the equation of the line first?

[slate monolith]

yes yes

find the slope between A and B

intrecept is A

[wicked axle]

$m=\frac{r-sqrt\left(r^2-\frac{r^4}{4}\right)}{-\frac{r^2}{2}}?$

[ocean seal]

Pahul's Uncle

[wicked axle]

that what im getting for slope lol

not simplified but yeah i think im doing it wrong

[queen wigeon]

thats what i got too

[wicked axle]

oh :o

so maybe it's right

@slate monolith can you confirm?

[slate monolith]

um

ur syntax is confusing me

usually do the greater x first

so (x-1)^2 + y^2 - 1 = x^2 + y^2 - r^2

-2x = - r^2

x = r^2/2

so

this gets messy

[queen wigeon]

wait, doesnt x = $r^2/2$

[slate monolith]

r^2/2 + y^2 = r^2

[ocean seal]

mchen10

[slate monolith]

mb mb+

[wicked axle]

yeah

i got x = r^2/2

[slate monolith]

yeah yeah

so r^4/4 + y^2 - r^2 = 0

[wicked axle]

yeah got that

[slate monolith]

looks good

[slate monolith]

👍

[wicked axle]

and we know the y intercept is r

[slate monolith]

ye

so y = mx + r

[crystal tapir]

pls help @here

[slender forge]

An easy way to do this is to pick a point (or probably several) on the given graph look at its slope then plug in that point(s) into each of the choices and see if it matches

[crystal tapir]

oki lemme try thx

[slate monolith]

ideally check the 0 values first

see if as u change x or y its constant or changing

or inc/decreasing

[summer goblet]

Yes. Try this.

[summer goblet]

And find a point where you can easy find the derivative visually.

[crystal tapir]

how do i do this @here

[crystal tapir]

yea thx i got it

[fringe yoke]

Is this an exam? It sais 1 mark

[slate monolith]

could be hw

dont ping here or anything

dont ping anyone unless u waited 15 min for helper

[crystal tapir]

srry m8

[crystal tapir]

yea its a vce past paper

2020

tech free

[slate monolith]

ah

is this calc @crystal tapir

so from what i understand

g'(x) = 2x

so g = x^2

[jagged imp]

@here is disabled by the way, just post your question and if it doesnt get answered for 15 mins you can ping helpers

[slate monolith]

mhm

[jagged imp]

arent vce marking guides all available online?

yeah the marking guide for this exam is here https://www.vcaa.vic.edu.au/assessment/vce-assessment/past-examinations/Pages/Mathematical-Methods.aspx

in case you need help on any other questions in future

oh this doesnt give working though since its one mark

nvm

[crystal tapir]

yea but it doesnt show working

[alpine sable]

can somebody explain question 3

i know the answer

but idk how exactly it works

[slate monolith]

4x3

3 busses or walk

then 3 buisses

[alpine sable]

ermm why

[slate monolith]

read above

[alpine sable]

oh hmmm

i get it i think

[rugged bronze]

Find all values of $x$ such that
$$\frac{x^2 + x + 3}{2x^2 + x - 6} \ge 0.$$
Note: Your solution should be thorough, and explain why all your values are the only values that satisfy the inequality.

[ocean seal]

MathMemer

[rugged bronze]

writing problem for aops

[slate monolith]

whats ur question

[indigo jetty]

@rugged bronze what have you done so far?

[gritty gull]

"A group of 4 students went to drink pearl tea and study at a local tea shop. The shop offers 12 different flavors of pearl tea. What is the probability that at least 2 students ordered the same flavor? Express your answer as a decimal, and round to the nearest ten thousandths."

May anyone explain this question please? It's on my Algebra 2 quiz and I'm really stressing out about it

[woven pollen]

One minus they all pick a different tea. 1 - [(1/12) * (1/11) * (1/10) * (1/9)]

S = {all different, at least two}. So 1 - P(all different) = P(atleast two)

note: 'at least 2' contains many more combinations, but in this case we do not have to worry about enumerating them.

e.g. 'exactly 3' is in 'at least 2'.

[fierce summit]

what i dont think it would be that high

[woven pollen]

yay, it will be high. because it includes at least 3 + at least 4 + exactly 3 + exactly 4.

meaning, at least 2 also includes they all order the same tea, etc

[fierce summit]

probably not about 99.99% as answer tho

maybe its actually 1 - [(12/12) * (11/12) * (10/12) * (9/12)]

[woven pollen]

OH! YES. Ooops.

😊

[fierce summit]

[tired locust]

I wanted to prove that the top compound proposition is a tautology by using logical equivalences. Does my work look correct here? (CDE = conditional-disjunction equivalence here)

[woven pollen]

Yes.

[tired locust]

Woot! I worked on this for longer than I care to admit.

Thanks for taking a look

[woven pollen]

yay. those things take forever.

[tired locust]

Every time I made a tiny error and had to scrap and start from scratch

[woven pollen]

I remember have to prove +0 = -0. it was like 4 lines and it took me about 4 hours to build.

[tired locust]

I'm always amazed at how much working on problems helps solidify. Every time I think about being lazy and skipping the exercises, I remember how valuable they are

[tired locust]

😮 that sounds way harder lol

[gritty gull]

oh alright, then the probability would be equivalent to <0.4721

[dim falcon]

seriously the last rule of this server is kinda pointless

i mean, it kinda makes you think... my major my choices lmao

[wide fern]

hey guys ive been working on this question for robotics for the past few hours

from what i remember, i need to use the lagrangian, except im not fully sure how to do it

[slate monolith]

aye physics

ur better asking this in the physics discord but

Kinetic energy is 1/2 mv^2

is that a spring

so ma = F - kx

a = dv/dt

do u have an idea of what im doing

[visual kernel]

what are the solution for task 1 and 2